A little bit of logic
One can only read if one has learnt to write! So both reading and writing are actions which we learn simultaneously!
On the illiterates of the Prophet
The Verse which underlines the illiterates of Mohammad (Peace be upon him) is (29:48) where the word used is تَتْلُو instead of تقرأ! Which means read and recite loudly. But from this Verse we can only conclude the certainty that Mohammad (Peace be upon him) was at least illiterate at the beginning of the revelation! Any time later needs strong evidence.
I strongly recommend you to read different translations as some translators used read while others used recite etc.!
Note that surat al-'Ankabut is makki and the 85th surah revealed according this link!
On the meaning of اقرأ
According to many Fatwas (I'll quote them later):
This word or the order "اقرأ" is used in Arabic in two different meanings:
- to express the process of reading (from) a written text.
This is the meaning used in Verse (17:14): as anyone of us would be asked to read what from his record on Judgement day! And as we might not know or have forgotten what we committed we are not prepared to recite it from our memory, so we may need to read it!
- to express the process of reciting from ones memory.
Here we have many examples from Quran like (16:98) and (75:17-18). But for the Verse of surat an-Nahl the meaning in my opinion differs according to the person who will recite or read Quran if it's a hafidh/hafiz then he might recite from his memory if it's not a hafiz he may read the text!
"Al-‘Allaamah Taahir ibn ‘Ashoor (may Allah have mercy on him) says:
The word “Iqra’ (read or recite)” is a command to read or recite. This word refers to speaking particular words that are either written or memorized by heart.
He afterwards quoted the Hadith of 'Aisha (May Allah be pleased with her)
then he concluded:
It was in this sense that the angel said to him on the three occasions “Iqra’ (read or recite),” repeating the phrase that had been revealed by Allah, and it was a repetition intended to put him at ease with a recitation that he had not learned before.
No object is mentioned for the verb “read” (or “recite”), either because it came in the form of an intransitive verb; or it was because what was to be read or recited was clear from the context, and what was meant was: recite what We are going to send down to you of the Qur’an. "
From this we can conclude that the meaning of اقرأ here is recite from your memory:
As Mohammad (Peace be upon him) was asked several times to recite/read, he then understood that he was not meant to read something rather then to recite what he has been told/taught and repeated it. So he didn't disobey the first order which was given to him at all, but followed it once he knew what this order was all about!
About Verse (29:38) ibn 'Ashoor said that this Verse explicitly neglected the writing and reading/recitation to show and clear any possible doubt that the Messenger of Allah (Peace be upon him) was illiterate!
See also this Fatawa in Arabic, English and again in Arabic.
And Allah knows best!